#4638 ⟨
a
,
b
|
aababaab
=
abb
⟩
Up:
Monoid enumeration
Prev:
#4637
⟨
a
,
b
|
aababaab
=
aba
⟩
Next:
#4639
⟨
a
,
b
|
aababaab
=
baa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ab
)
2
a
2
b
=
a
b
2
and
a
⋅
b
2
=
a
b
2
, however (
ab
)
2
a
2
b
≠
b
2
Not right cancellative, because right multiplication by
b
is not injective:
a
(
ab
)
2
a
2
⋅
b
=
a
b
2
and
ab
⋅
b
=
a
b
2
, however
a
(
ab
)
2
a
2
≠
ab
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
(
ab
)
3
b
⇒
a
b
2
ab
a
2
b
[2]
2.
a
(
ab
)
2
a
2
b
⇒
a
b
2
[1]
# ab:aababaab=abb ba - - aabababb=abbabaab aababaab=abb